Finite Group Databasebeta

← #14665778

Subgroups — #14665778

Order 2816.

234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66890C211yesmaximal, characteristic
2#13067501C211yesmaximal, characteristic, complemented
3#13067500C211yesmaximal, characteristic, complemented
4#13066689C211yesmaximal, characteristic, complemented
5#13066578C211yesmaximal, characteristic, complemented
6#13066532C211yesmaximal, characteristic, complemented
7C11×#1331C211yesmaximal, characteristic, complemented
8C4×C11×D8C2211yescharacteristic
9C2×#66890C411yescharacteristic
10#10622625—21no—
11#10622451—21no—
12C4×D88C2211yescharacteristic
13C4×C11×C16C2211yescharacteristic
14C11×#335C2211yescharacteristic
15#10622200C411yescharacteristic
16D4⋊(C11⋊C8)—21no—
17#10622129C411yescharacteristic
18#10622127C411yescharacteristic
19#10622121—21no—
20C4×C11⋊C16C2211yescharacteristic
21#10622096C2211yescharacteristic
22C8×C11⋊C8C2211yescharacteristic
23C2×C11×D8C2×C411yescharacteristic
24C4×D4×C11—21no—
25C2×#4318—41no—
26C2×D88C2×C411yescharacteristic
27C2×#4313—41no—
28C4×D44—21no—
29C2×C11×C16—21no—
30C11×#107C2×C411yescharacteristic
31C11×C4⋊C8—21no—
32C11×#102—21no—
33C4×C8×C11C2311yescharacteristic
34C22⋊(C11⋊C8)—41no—
35#66890—22no—
36#66885—21no—
37(C2×D11)⋊C8—41no—
38#66882C2×C411yescharacteristic
39C2×C11⋊C16C2×C411yescharacteristic
40C2×C11⋊C16C2×C411yescharacteristic
41C4⋊(C11⋊C8)—21no—
42C4×C11⋊C8D411yescharacteristic
43C4×C11⋊C8D411yescharacteristic
44#12086—111nomaximal, Sylow
45C2×D4×C11—21no—
46C22×C4×C11—41no—
47C2×D44—21no—
48C2×C4×D11—41no—
49C11×D8—21no—
50C11×D8—21no—
51C2×C8×C11—41no—
52C2×C8×C11C22×C411yescharacteristic
53C2×C8×C11#4111yescharacteristic
54C11×C4⋊C4—21no—
55C11×C22⋊C4—41no—
56C42×C11C2×D411yescharacteristic
57(C2×D11)⋊C4—41no—
58C4⋊Dic11—21no—
59#4318—82no—
60C2×C11⋊C8—21no—
61C2×C11⋊C8—41no—
62C2×C11⋊C8D811yescharacteristic
63C2×C11⋊C8D811yescharacteristic
64D88—21no—
65D88—21no—
66#4313—82no—
67C11×C16—22no—
68C11⋊C16—21no—
69C11⋊C16M1612yescomplemented
70C4×D16—111no—
71#1589—111no—
72#1589—111no—
73#1372—111no—
74#1331—111no—
75#1331D1111yescharacteristic, complemented
76#1311—111no—
77C23×C11—41no—
78C22×D11—41no—
79D4×C11—41no—
80D4×C11—41no—
81C2×C4×C11—41no—
82C2×C4×C11—81no—
83C2×C4×C11—81no—
84C2×C4×C11C4×D411yescharacteristic
85C2×C4×C11C2×D811yescharacteristic
86C2×C4×C11#13511yescharacteristic
87C2×Dic11—41no—
88D44—41no—
89D44—41no—
90C4×D11—81no—
91C4×D11—81no—
92C8×C11—21no—
93C8×C11—81no—
94C8×C11C2×M1611yescharacteristic
95C8×C11#13111yescharacteristic
96C11⋊C8—21no—
97C11⋊C8—21no—
98C11⋊C8—41no—
99C11⋊C8—81no—
100C2×D16—111no—
101C4×D8—111no—
102C4×D8C2×D1111yescharacteristic
103#436—221no—
104#436—221no—
105#366—111no—
106#357—111no—
107#357—111no—
108C4×C16—111no—
109C4×C16C2×D1111yescharacteristic
110#335—111no—
111#335C2×D1111yescharacteristic
112D4⋊C8—221no—
113D4⋊C8—221no—
114C82—111no—
115C22×C11—81no—
116C22×C11—81no—
117C22×C11—81no—
118C22×C11C4×D811yescharacteristic
119C2×D11—81no—
120C2×D11—81no—
121C2×D11—81no—
122C4×C11—21no—
123C4×C11—81no—
124C4×C11#43611yescharacteristic
125C4×C11#44311yescharacteristic
126C4×C11#50911yescharacteristic
127C4×C11#50911yescharacteristic
128Dic11—81no—
129C2×D8—111no—
130C2×D8C4×D1111yescharacteristic
131C2×M16—441no—
132C2×M16—441no—
133C4×D4—21no—
134C4×D4—221no—
135D16—222no—
136C2×C16—21no—
137C2×C16—111no—
138C2×C16—111no—
139#107—111no—
140#107C4×D1111yescharacteristic
141C4⋊C8—21no—
142C4⋊C8—221no—
143#102—21no—
144#102—221no—
145C22⋊C8—441no—
146C22⋊C8—441no—
147C4×C8—111no—
148C4×C8—111no—
149C4×C8C22×D1111yescharacteristic
150C2×C11—161no—
151C2×C11#158911yescharacteristic
152C2×C11#217711yescharacteristic
153C2×C11#217911yescharacteristic
154D11—161no—
155C2×D4—21no—
156C2×D4—221no—
157C22×C4—41no—
158C22×C4—441no—
159D8—21no—
160D8—21no—
161D8—221no—
162D8—221no—
163M16—882no—
164M16—882no—
165C2×C8—41no—
166C2×C8—111no—
167C2×C8—111no—
168C2×C8—221no—
169C2×C8—441no—
170C2×C8C2×C4×D1111yescharacteristic
171C2×C8#434111yescharacteristic
172C4⋊C4—21no—
173C4⋊C4—221no—
174C22⋊C4—41no—
175C22⋊C4—441no—
176C42D4×D1111yescharacteristic
177C16—22no—
178C16—112no—
179C16—221no—
180C11#1208611yescharacteristic, complemented, Sylow
181C23—41no—
182C23—441no—
183D4—41no—
184D4—41no—
185D4—441no—
186D4—441no—
187C2×C4—41no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—441no—
191C2×C4—881no—
192C2×C4—881no—
193C2×C4(C22⋊D11)⋊C411yescharacteristic
194C2×C4D8×D1111yescharacteristic
195C2×C4#6696911yescharacteristic
196C8—21no—
197C8—81no—
198C8—221no—
199C8—221no—
200C8—441no—
201C8—881no—
202C8#6695411yescharacteristic
203C8M16×D1111yescharacteristic
204C22—81no—
205C22—81no—
206C22—81no—
207C22—881no—
208C22—881no—
209C22—881no—
210C22#1062236911yescharacteristic
211C4—21no—
212C4—81no—
213C4—881no—
214C4#1062234211yescharacteristic
215C4#1062243711yescharacteristic
216C4#1062252411yescharacteristic
217C4#1062252711yescharacteristic
218C2—161no—
219C2—1761no—
220C2#1306749811yescharacteristic
221C2#1307048911yescharacteristic
222C2#1307049911yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#1331C2
socleC22×C11C4×D8
prime radicalC2×#66890C4
cosocleC4×C8×C11C23
hypercenter#1331D11
hypocenterC11#12086
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13067501C2semidirect
3. #13067500C2semidirect
4. #13066689C2semidirect
5. #13066578C2semidirect
6. #13066532C2semidirect
7. C11×#1331C2semidirect
69. C11⋊C16M16semidirect
75. #1331D11semidirect
180. C11#12086semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×#668902
#130675012
#130675002
#130666892
#130665782
#130665322
C11×#13312
#1208611